Simplify the following expression and state the condition under which the simplification is valid: $p = \dfrac{t^2 - 10t + 9}{t^2 - 9t}$
First factor the expressions in the numerator and denominator. $ \dfrac{t^2 - 10t + 9}{t^2 - 9t} = \dfrac{(t - 1)(t - 9)}{(t)(t - 9)} $ Notice that the term $(t - 9)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(t - 9)$ gives: $p = \dfrac{t - 1}{t}$ Since we divided by $(t - 9)$, $t \neq 9$. $p = \dfrac{t - 1}{t}; \space t \neq 9$